Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#486 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #486 | D43 |
| hypocenter | C43 | #3295 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583610 | C2 | semidirect |
| 3. #14583216 | C2 | semidirect |
| 4. #14583186 | C2 | semidirect |
| 5. #14583127 | C2 | semidirect |
| 6. #14583096 | C2 | semidirect |
| 7. #14583051 | C2 | semidirect |
| 8. C4×#10621873 | C2 | semidirect |
| 9. C8×D172 | C2 | semidirect |
| 10. #102×D43 | C2 | semidirect |
| 11. C43×#486 | C2 | semidirect |
| 15. C2×#10621883 | C22 | semidirect |
| 16. C2×C8×D43 | C22 | semidirect |
| 18. #13063305 | C22 | semidirect |
| 23. C4×Dic86 | C22 | semidirect |
| 27. C4⋊C4×D43 | C22 | semidirect |
| 28. #13063257 | C22 | semidirect |
| 29. #13063256 | C22 | semidirect |
| 30. C4⋊(C43⋊C8) | C22 | semidirect |
| 31. #13063250 | C22 | semidirect |
| 33. #13063246 | C22 | semidirect |
| 35. (C2×D43)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C43 | C22 | semidirect |
| 38. #102×C43 | C22 | semidirect |
| 39. #102×C43 | C22 | semidirect |
| 40. C4×C8×C43 | C22 | semidirect |
| 99. D172 | SD16 | semidirect |
| 139. #486 | D43 | semidirect |
| 148. C43 | #3295 | semidirect |
| 154. C4⋊Q8 | C2×D43 | semidirect |
| 174. #102 | C2×D43 | semidirect |
| 175. #102 | C2×D43 | semidirect |
| 177. C4×C8 | C2×D43 | semidirect |